Abstract

Let C , D and E be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor C ! D , i.e., a functor 2 q\Omega C ! D , induce a right q-transfor C ! D , i.e., a functor C\Omega 2 q ! D ? More generally, does a functor C\Omega D ! E induce a functor D\Omega C ! E? For c; c 0 elements of C whose (k \Gamma 1)-sources and (k \Gamma 1)-targets agree, does a q-transfor C ! D induce a q-transfor C (c;c 0 ) ! D (d;d 0 ), for appropriate d;d 0 2 D ? For c; c 0 2 C and d;d 0 2 D whose (k \Gamma 1)-sources and (k \Gamma 1)-targets agree, does a q-transfor C\Omega D ! E induce a (q+k+1)-transfor C (c;c 0 )\Omega D (d;d 0 ) ! E(e;e 0 ), for appropriate e; e 0 2 E? I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and in some cases for n up to 5 which do not need all data and axioms...

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